MATH 300 COMPUTATIONAL METHODOLOGIES 3.0: 3 cr. E
In this course, students are introduced to key computational techniques used in modeling and simulation of real-world phenomena. The computer- based simulations and modeling are becoming increasingly accepted as viable, efficient, quick, and cost effective means to study real world problems. The emphasis here is not so much on programming technique, but rather on understanding basic concepts and principles. Employment of higher level programming and visualization tools, such as Mathematica or MATLAB, introduces a powerful tool set commonly used by the industries and academia. One of them, or both, will be used as programming platforms for this course. Elements of computer visualization and Monte Carlo simulation will be discussed.
MATH 310 COMPUTATIONAL GEOMETRY II 3.0: 3 cr. E
3D geometrical modeling of curves and surfaces; Bezier, B-Spline and NURBS modeling; hidden surface elimination algorithms (Painter algorithm, Robert algorithm, Z-buffer algorithm); color theory, illumination and shading models, rendering, texture; introduction to ray tracing; morphing; virtual reality.
Project in C++ or Java.
MATH 311(CSIS 350 ) DIGITAL IMAGE PROCESSING AND APPLICATIONS 3.0: 3 cr. E
Image acquisition and storage; imaging geometry: transformations and camera models; image transforms: Fourrier Transform and Fast Fourrier Transform; image enhancement in frequency domain and spatial domain; image restoration, compression and segmentation.
Project in C++ or Java. Prerequisite: MATH 310.
Faculty of Sciences 33
MATH 312 BIOMETRICS 3.0: 3 cr. E
Biometrics deals with identification of individuals based on their biological or behavioral characteristics. This course lays out the basics of biometric concepts, techniques, tools, and applications to recognize or verify the identity of individuals from traits of the face, voice, fingerprints, retina, iris, signatures, and hand geometry, among other modalities. Multi-modal biometric systems that use two or more of these characteristics are discussed. Biometric system performance and issues related to the security and privacy aspects of these systems are also addressed.
Prerequisites: Graduate standing, or senior standing with the permission of the instructor or department. A background in probability and statistics, pattern recognition and image processing would be useful
MATH 313 MATHEMATICS OF MEDICAL IMAGING 3.0: 3 cr. E
At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data.
This course provides a firm foundation in the mathematical and physical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities like X-ray computed tomography, nuclear medicine (SPECT/PET), and magnetic resonance imaging (MRI). In the process, it also covers many important analytic concepts, and techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis. Moreover, this course treats several numerical applications simulating the process of medical image reconstruction.
MATH 314 - ADvANCED IMAGE AND vIDEO PROCESSING 3.0: 3 cr. E
This is an advanced course that provides students with an insight to advanced digital image and video processing theory and techniques. Topics include: Image and video compression, spatial processing, image restoration, image segmentation, Geometric PDE’s, image and video inpainting, sparse modeling and compressed sensing, and medical imaging.
MATH 320 CHAOTIC DYNAMICAL SYSTEMS 3.0: 3 cr. E
Hyperbolicity; symbolic dynamics, topological conjugacy, chaos,; Sarkovskii’s theorem; bifurcation theory, maps of circle, the period-doubling route to chaos; kneading theory, horseshoe map; hyperbolic toral automorphism.
Applications with Mathematica software.
MATH 321 FRACTALS AND IMAGE COMPRESSION 3.0: 3 cr. E
Metric spaces, transformations on metric spaces; contraction mapping chaotic dynamics on fractals; fractal dimensions, fractal interpolation; Julia sets and Mandelbrot sets; measures on fractals; iterated function system. Applications with Chaoscope software.
Prerequisite: MATH 320.
MATH 332 FINITE DIFFERENCES, FINITE ELEMENTS AND APPLICATIONS 3.0: 3 cr. E
The finite difference methods approximate a partial differential equation problem by an algebraic problem through the replacement of the derivatives by finite differences as given by Taylor series expansion. The finite element methods approximate the solution of a partial differential equation by a numerical solution that belongs to a finite dimensional vector space of known basis.
MATH 340 MULTIvARIATE STATISTICS 3.0: 3 cr. E
Multiple regression; factor analysis; principal components analysis; hierarchical cluster and k-means. Applications with SPSS software.
MATH 341 (CSIS362) NEURAL NETwORKS AND APPLICATIONS 3.0: 3 cr. E
architectures and equilibrium. The Hopfield model and recurrent networks. The self- organizing map. Adaptive resonance theory.
Project in C++ or Java.
MATH 343 TIME SERIES AND FORECASTING 3.0: 3 cr. E
Least squares smoothing and prediction; linear systems; Fourier analysis, and spectral estimation; impulse response and transfer function; detection of seasonality, autocorrelation function, Fisher method; exponential smoothing, Holt-Winters methods; AR, MA , ARMA processes.
Applications with Eviews software. Prerequisite: MATH 340.
MATH 350 GRAPH THEORY AND APPLICATIONS 3.0: 3 cr. E
This course focuses on the mathematical theory of graphs; Topics include trees, connectivity, Eulerian and Hamiltonian graphs, matchings, edge and vertex colorings, independent sets and cliques, planar graphs and directed graphs; graph coloring; algorithms and complexity; embedding graphs on surfaces; graph minors; probabilistic methods and random graphs. Applications with Mathematica software.
MATH 360 RIEMANNIAN GEOMETRY 3.0: 3 cr. E
Riemannian Geometry provide an important tool in modern mathematics impacting on diverse areas from the pure to the applied. The objects of this course are smooth manifolds equipped with extra structures that provide geometric information. In particular, we will study a manifold with a Riemannian metric that allows measurement of quantities such as distance and angle, and an affine connection. This course describes the notion of geodesics and curvature and analyzes manifolds with constant curvature, with a focus on the sphere and hyperbolic space.
MATH 390 MASTER’S PROJECT 3.0 cr. E MATH 399 MASTER’S THESIS 6.0 cr. E